Solving Evaluate

Evaluate: It is a process of simplifying an equation in algebra. Algebraic equations are of many types like monomial, polynomials trinomials etc. The polynomial equations are solved by the two ways.Evaluation is the process of solving the equations for particular variables. The methods of solving algebra equation in polynomial are:

Evaluate by Substitution method or plug-in equation method
Elimination method or addition or subtraction method.


Equation evaluation:

Solving by substitution method:

The steps taken in the substitution method or plug-in equation method are as follows,

First solve any one equation for a variable in the given pair of equations.
Then plug the variable into the next equation and solve it.
The equation will be solved for a variable.
Then plug-in the value of the variable in anyone of the equations.
Then solve the next variable in the equation by plugging the value of the variable.
Now repeat the above steps to solve any of the equations left in the variable in the equation.

So, we get the solution for the equations by solving. For evaluating, we mainly use substitution method.

Solving by elimination method:

The steps followed in the elimination method are follows as:

First make one equation equal to others part of the equation.
Then eliminate the variable in the next equation and solve it for the next variable.
The equation will be solved for a variable.
Then plug-in the value of the variable for anyone of the equations.
Then solving the next variable in the equation by plugging the value in the variable.
Now repeat the above steps to solve any of the equations evaluate left in the variable in the equation.

So, we get the solution for the equations by solving. For evaluating, we mainly use substitution method.



Solving Evaluate:Example problems

Example for substitution method:
Evaluate:
4x + 3y = 36 => (1)
y =8               => (2)
Solution:
Substitute equation (2) in equation (1)
4x + 3(8) = 32
4x +24 = 32
-24  -24
4x = 8
Here 24 is subtracted from both sides and part of the equation has been reduced.
4x = 8
On dividing by 4 on both side we get,
x = 2
So, the equation is reduced to obtain the solution.

Example for elimination method:
Evaluate:
2x= I + 5y,
2x+3y-9=0
Solution:
The given equations may be written as
2x - 5y = l ------ (1)
2x + 3y = 9 ----- (2)
(-)   (-)      (-)
On Subtracting we get, - 8y = - 8
Divide by  -8 on both sides,
Y=(-1)/(8) *(-8) =1
Y=1
By substituting y=1 in equation (2),we get
2x+3y=9
2x+3(1) =9
2x+3=9
2x=9-3=6
X=(1)/(2) *(6) =3
X=3
X=3, y=1 is the solution